Number of 1 Bits 位1的个数

本文介绍了一个函数,该函数接收一个无符号整数作为输入,并返回其二进制表示中1的个数,即汉明重量。通过与运算检查每一位是否为1来实现计数。

编写一个函数,输入是一个无符号整数,返回其二进制表达式中数字位数为 ‘1’ 的个数(也被称为汉明重量)。

示例 :

输入: 11
输出: 3
解释: 整数 11 的二进制表示为 00000000000000000000000000001011 

示例 2:

输入: 128
输出: 1
解释: 整数 128 的二进制表示为 00000000000000000000000010000000

思路:这道题就逐个和1做与运算,如果结果是1就累加到res上即可。

参考代码:

    int hammingWeight(uint32_t n) {
	int i = 1;
	int res = 0;
	while (i <= 32) {
		if (n & 1) {
			res++;
		}
		n = n >> 1;
		i++;
	}
	return res;      
    }



编写一个函数,输入是一个无符号整数,返回其二进制表达式中数字位数为 ‘1’ 的个数(也被称为汉明重量)。

示例 :

输入: 11
输出: 3
解释: 整数 11 的二进制表示为 00000000000000000000000000001011

 

示例 2:

输入: 128
输出: 1
解释: 整数 128 的二进制表示为 00000000000000000000000010000000
### LeetCode Problems Involving Counting the Number of 1s in Binary Representation #### Problem Description from LeetCode 191. Number of 1 Bits A task involves writing a function that receives an unsigned integer and returns the quantity of '1' bits within its binary form. The focus lies on identifying and tallying these specific bit values present in any given input number[^1]. ```python class Solution: def hammingWeight(self, n: int) -> int: count = 0 while n: count += n & 1 n >>= 1 return count ``` This Python code snippet demonstrates how to implement the solution using bitwise operations. #### Problem Description from LeetCode 338. Counting Bits Another related challenge requires generating an output list where each element represents the amount of set bits ('1') found in the binary notation for integers ranging from `0` up to a specified value `n`. This problem emphasizes creating an efficient algorithm capable of handling ranges efficiently[^4]. ```python def countBits(num): result = [0] * (num + 1) for i in range(1, num + 1): result[i] = result[i >> 1] + (i & 1) return result ``` Here, dynamic programming principles are applied alongside bitwise shifts (`>>`) and AND (`&`) operators to optimize performance during computation. #### Explanation Using Brian Kernighan Algorithm For optimizing further especially with large inputs, applying algorithms like **Brian Kernighan** offers significant advantages due to reduced iterations needed per operation compared against straightforward methods iterating through all possible positions or dividing repeatedly until reaching zero. The core idea behind this method relies upon subtracting powers-of-two corresponding only to those places holding actual ‘ones’ thereby skipping over zeroes entirely thus reducing unnecessary checks: ```python def hammingWeight(n): count = 0 while n != 0: n &= (n - 1) count += 1 return count ``` --related questions-- 1. How does the Hamming weight calculation differ between signed versus unsigned integers? 2. Can you explain why shifting right works effectively when determining counts of one-bits? 3. What optimizations exist beyond basic iteration techniques for calculating bit counts? 4. Is there any difference in implementation logic required across various programming languages supporting similar syntaxes? 5. Why might someone choose the Brian Kernighan approach over other strategies?
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